Finite Group Databasebeta

← Prev (#22551234) Next (#22551236) →

C3×C5×D7×C13⋊C3 #22551235

order8190
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×D7×C13⋊C3

Splittings

Fitting, socleC3×C5×C7×C13 ⋊ C2×C3
derived, HallC7×C13 ⋊ C2×C32×C5
HallC3×C5×C7×C13⋊C3 ⋊ C2
HallC5×C13×D7 ⋊ C32
HallC3×C7×C13⋊C3 ⋊ C2×C5
HallC5×C7×C13 ⋊ C2×C32
HallC13×D7 ⋊ C32×C5
HallC5×C13 ⋊ C32×D7
HallC5×C7 ⋊ C2×C3×C13⋊C3
SylowC13 ⋊ C32×C5×D7
SylowC7 ⋊ C2×C3×C5×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C5D7×C13⋊C3
commutator, hypocenterC7×C13C2×C32×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C13C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C3×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

525 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×D7×D13⋊C3, C3×D7×C5⋊(D13⋊C3), C3×D5×D7×C13⋊C3, …
maximal normal subgroup ofC3×C5×D7×D13⋊C3, C3×D7×C5⋊(D13⋊C3), C3×D5×D7×C13⋊C3, …
maximal quotient ofC3×C5×Dic7×C13⋊C3, C2×C3×C5×D7×C13⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8190, 69);